Deriving Target Selection Rules from Endogenously Selected Samples

One of the aims of direct marketing in practice is to target the most profitable customers in the database at hand. This selection is often done based on observed behavior in the past. As a consequence, databases arising from the responses to direct mailings are not a random sample from all potential respondents. When not all heterogeneity is observed, part of the target selection rule will be based on the unobserved heterogeneity, so selection is endogenous. Treating an endogenously selected sample as a random sample results in inconsistent parameter estimates, which in general also harms the predictive performance of the model. We develop an adjustment to the likelihood of the model that corrects for the endogenous sample selection. We apply this technique to the selection of mail targets for a charitable organization. In the application we also show that, based on a model for the response rate and the amount donated simultaneously, we can create a target selection rule that maximizes expected revenues. Such a selection rule outperforms selection rules based on response rates or donated amount only. The traditional approach of maximizing response is therefore not the optimal approach to target selection.